Position an oven rack in the center of the oven and preheat to 350 degrees F.
Cook the pasta to al dente according to the package directions. (Reserve some pasta water to add back in case the dish needs moisture.)
Melt 2 tablespoons butter in a large skillet over medium-high heat and add the garlic. Cook, stirring occasionally, until very fragrant but not browned, about 1 minute. Add the cream and Parmesan and cook, stirring frequently until the mixture begins to boil, about 5 minutes. Add the chicken and cooked pasta and carefully toss to completely coat, then continue to cook until the mixture is smooth and thick, about 3 minutes. Season with salt and pepper and add the remaining 6 tablespoons butter. Carefully stir until the butter is completely melted and the sauce is glossy and creamy; remove from the heat.
Alternating 1 slice of tomato and 1 slice of mozzarella, shingle around the outer edge of the skillet creating a ring that covers the pasta. Repeat with the remaining tomato and mozzarella forming smaller concentric rings until the pasta is completely covered. Drizzle with the olive oil, sprinkle with some salt and bake until the mozzarella is beginning to melt but the slices still hold their shape and are still white, about 20 minutes. Let cool 10 minutes, then top with the basil and serve.
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